GCF of 2822/224, 8314/226
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2822/224, 8314/226 i.e 2/25312 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2822/224, 8314/226.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 2822/224,8314/226?
Given fractions are 2822/224,8314/226
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 2822/224,8314/226, numerators are 2822,8314
Denominators are 224,226
The GCF of 2822,8314 is 2 .
LCM of 224,226 is 25312.
The greatest common factor of 2822/224,8314/226 = [GCF of 2822,8314]/[LCM of 224,226]= 2/25312
Therefore, the GCF of 2822/224,8314/226 is 2/25312.
To find the highest common factor of 2822,8314, we have to find the factors of both numbers and list the highest common factor.
The factors of 2822 are 1, 2, 17, 34, 83, 166, 1411, 2822
The factors of 8314 are 1, 2, 4157, 8314
The HCF of 2822,8314 is 2.
Lets's calculate GCF of 2822,8314
| 2 | 2822, 8314 |
| 1411, 4157 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2822,8314 By Matching Biggest Common Factor Method
Now, list down the factors of 2822
:1,2,17,34,83,166,1411,2822
Now, list down the factors of 8314
:1,2,4157,8314
Greatest Common Factor
We found the factors 2822,8314 . The biggest common factor number is the GCF number.
So the greatest common factor 2822,8314 is 2.
Lets's calculate LCM of 224,226
| 2 | 224, 226 |
| 112, 113 |
∴ So the LCM of the given numbers is 2 x 112 x 113 = 25312
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/25312
Therefore, the GCF of Fractions 2822/224,8314/226 is 2/25312
Least Common Multiple of 224,226 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 224,226 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(224,226) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(224,226) x common factors =2 x 1 = 2
LCM(224,226) = ( 224 × 226 ) / 2
LCM(224,226) = 50624 / 2
LCM(224,226) = 25312
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FAQs on GCF of Fractions of 2822/224, 8314/226
1. What is the HCF of 2822,8314?
The HCF of 2822,8314 is 2
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 2822/224, 8314/226?
Answer: GCF of Numerators as per given numbers 2822/224, 8314/226 is
GCF of Numerators i.e. for 2822,8314 is 2
LCM of denominators i.e. for 224,226 is 25312.
Thus, GCF of Fractions is 2/25312.Finally, GCF of Fractions for 2822/224, 8314/226 is 2/25312.